منابع مشابه
On Scalar-valued Nonlinear Absolutely Summing Mappings
w,q = supφ∈BX́ ( ∑k j=1 | φ(xj) | ) 1 q . This is a natural generalization of the concept of (p; q)-summing operators and in the last years has been studied by several authors. The infimum of the L > 0 for which the inequality holds defines a norm ‖.‖as(p;q) for the case p ≥ 1 or a p-norm for the case p < 1 on the space of (p; q)-summing homogeneous polynomials. The space of all m-homogeneous (p...
متن کاملCotype and Non Linear Absolutely Summing Mappings
In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every n-linear mapping from L∞-spaces into K is (2; 2, ..., 2,∞)-summing and also shown that every n-linear mapping from L∞-spaces into F is (q; 2, ..., 2)-summing whenever F has cotype q. We also give new examples of analytic summing mappings and polynomial...
متن کاملA Remark on Absolutely Summing Multilinear Mappings *
In this note we obtain new coincidence theorems for absolutely summing multilinear mappings between Banach spaces. We also prove that our results, in general, can not be improved.
متن کاملA General Extrapolation Theorem for Absolutely Summing Operators
The notion of absolutely (p; q)-summing linear operators is due to A. Pietsch [18] and B. Mitiagin and A. Pe lczyński [14], inspired by previous works of A. Grothendieck. The nonlinear theory of absolutely summing operators was initiated by A. Pietsch and a complete nonlinear approach was introduced by M.C. Matos [12]. Let X,Y be Banach spaces over a fixed scalar field K = R or C; for 1 ≤ p < ∞...
متن کاملAbsolutely Summing Operators on Non Commutative C-algebras and Applications
Let E be a Banach space that does not contain any copy of l and A be a non commutative C∗-algebra. We prove that every absolutely summing operator from A into E∗ is compact, thus answering a question of Pe lczynski. As application, we show that if G is a compact metrizable abelian group and Λ is a Riesz subset of its dual then every countably additiveA∗-valued measure with bounded variation and...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2007
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm178-1-2